Problem 49
Question
Write each English sentence as an equation in two variables. Then graph the equation. The \(y\) -value is three decreased by the square of the \(x\) -value.
Step-by-Step Solution
Verified Answer
The English sentence 'The \(y\) -value is three decreased by the square of the \(x\)' can be translated into the equation \(y = x^2 - 3\). The graph of this equation is a parabola opening upwards, with its vertex at (0,-3).
1Step 1: Translate English Sentence to Mathematical Equation
The English sentence 'The \(y\) -value is three decreased by the square of the \(x\)' can be translated into a mathematical equation as \(y = x^2 - 3\).
2Step 2: Plotting the Graph
The equation obtained, \(y = x^2 - 3\), needs to be plotted on a graph. The graph of a quadratic function such as this one is a parabola. In this case, the graph is a parabola that is translated 3 units down, which means that the vertex is at (0, -3). The graph opens upward, which tells you it's a positive quadratic. Plot points on both sides of the vertex to obtain as accurate a graph as possible.
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Problem 48
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